\[f_n=\frac{nv}{4(L+e)}\]
Variables
fnresonant frequency (Hz)
nodd harmonic number
vspeed of sound (m/s)
Lphysical pipe length (m)
eend correction at the open end (m)
Description
What is this formula?
The Resonant Frequency of a Closed Pipe formula calculates the natural frequencies of a pipe closed at one end and open at the other. A closed pipe has a displacement node at the closed end and a displacement antinode at the open end.
When to use it
Use this formula when analyzing closed air columns, clarinet-like instruments, acoustic resonators, and tube resonance experiments with one closed end.
Example
Given:
n = 1
v = 343 m/s
L = 0.25 m
e = 0.010 m
Formula:
fn = nv/(4(L + e))
Substitution:
fn = (1 × 343)/(4(0.25 + 0.010))
fn = 343/(4 × 0.260)
fn = 329.8 Hz
Result:
fn ≈ 329.8 Hz
Applications
Closed pipe resonators.
Clarinet acoustics.
Acoustic tube experiments.
Musical instrument design.
Standing wave analysis.